Many-Body Effects on the ${\rho }_{xx}$ Ringlike Structures in Two-Subband Wells

The longitudinal resistivity ${\rho }_{xx}$ of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density–magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory and linear response, we investigate the shape and spin polarization of these structures as a function of temperature and magnetic-field tilt angle. We find that (i) some of the rings “break” at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization ($\sim 50\%$) within, consistent with the NMR data of Zhang et al. [Phys. Rev. Lett. 98, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation effects leads to a collapse of the rings at some critical angle ${\theta }_c$, in agreement with the data of Guo et al. [Phys. Rev. B 78, 233305 (2008)].

Figure 1

Two-subband GaAs well and schematic fan diagram with LL crossings from distinct subbands. The $ABCD$ loop gives rise to ringlike structures in the calculated $n_{2\mathrm{D}}-B$ diagram of ${\rho }_{xx}$ (b) for $\nu =4$. This ring “breaks” at lower temperatures (c) due to quantum Hall ferromagnetic transitions, thus displaying a high spin polarization within (d) [12]. For increasing $B$ field tilt angles $\theta$, the ring shrinks (i.e., $A$ and $C$ move closer) and fully collapses ($A=C$) at ${\theta }_c$ (e), in agreement with the data 13 (cf. empty and solid circles).

Figure 2

(a) Longitudinal resistivity ${\rho }_{xx}$ calculated for $n_{2\mathrm{D}}=7.3\times {10}^{-11}{\mathrm{cm}}^{-2}$ [see horizontal dashed line in Figs. 1b, 1c] for $T=70\mathrm{mK}$ (dotted line) and $T=340\mathrm{mK}$ (solid line, slightly shifted upwards for clarity). Note the distinctive spike in the higher temperature ${\rho }_{xx}$ at $B\approx 7.6\mathrm{T}$. (b) and (c) show the corresponding Landau fan diagrams for low and high temperatures, respectively. Note that for $T=70\mathrm{mK}$, the LLs show discontinuities near $B=7.6\mathrm{T}$. These discontinuities suppress the ${\rho }_{xx}$ spike at $B\approx 7.6\mathrm{T}$ because the corresponding levels do not actually cross the chemical potential $\mu$—they suddenly jump over it. At higher temperatures the Landau diagram is continuous and the spike appears in ${\rho }_{xx}$.

Figure 3

Noninteracting (a)–(b) and interacting (c)–(d) Landau fan diagrams near the $\nu =4$ ring for several tilt angles, showing the anticrossings ($B$ and $D$) due to the inter-LL coupling, Eq. (4). For increasing $\theta$ the anticrossings near $D$ and $B$ become larger thus making $A$ and $C$ move closer and the ring shrink. The noninteracting model [25] gives a qualitative picture of the ring collapse, while our many-body calculation (c)–(d) ($T=70\mathrm{mK}$) provides a quantitative description and shows the relevance of competing XC effects, see Fig. 1e.